2025/05/30 by Paolo Braccia, N. L. Diaz, Braccia, Paolo +8 · 1 voice · 6 citations
Computer Science · Physics and Astronomy · #Quantum Information and Cryptography #Quantum Computing Algorithms and Architecture #Quantum optics and atomic interactions
paper · pdf · doi:10.48550/arxiv.2505.24212
Sampling unitary Fermionic Linear Optics (FLO), or matchgate circuits, has become a fundamental tool in quantum information. Such capability enables a large number of applications ranging from randomized benchmarking of continuous gate sets, to fermionic classical shadows. In this work, we introduce optimal algorithms to sample over the non-particle-preserving (active) and particle-preserving (passive) FLO Haar measures. In particular, we provide appropriate distributions for the gates of n-qubit parametrized circuits which produce random active and passive FLO. In contrast to previous approaches, which either incur classical O(n3) compilation costs or have suboptimal depths, our methods directly output circuits which simultaneously achieve an optimal down-to-the-constant-factor Θ(n) depth and Θ(n2) gate count; with only a Θ(n2) classical overhead. Finally, we also provide quantum circuits to sample Clifford FLO with an optimal Θ(n2) gate count.